- Email: [email protected]
Implementation of boundary conditions in modeling the femur is critical for the evaluation of distal intramedullary nailing
ARTICLE IN PRESS
JID: JJBE
[m5G;August 30, 2015;13:54]
Medical Engineering and Physics 000 (2015) 1–8
Contents lists available at ScienceDirect
Medical Engineering and Physics journal homepage: www.elsevier.com/locate/medengphy
Implementation of boundary conditions in modeling the femur is critical for the evaluation of distal intramedullary nailing Riza Bayoglu, A. Fethi Okyar∗ Department of Mechanical Engineering, Yeditepe University, Atasehir, Istanbul 34755, Turkey
a r t i c l e
i n f o
Article history: Received 24 January 2014 Revised 8 August 2015 Accepted 12 August 2015 Available online xxx Keywords: Intramedullary nail Retrograde stabilization Pre-clinical testing Distal femoral fracture Physiological boundary conditions Finite element method
a b s t r a c t In previous numerical and experimental studies of the intramedullary nail-implanted human femur several simplifications to model the boundary and loading conditions during pre-clinical testing have been proposed. The distal end of the femur was fixed in the majority of studies dealing with the biomechanics of the lower extremity, be it numerical or experimental, which resulted in obviously non-physiological deflections. Per contra, Speirs et al. (2007) proclaimed physiological deflections as a result of constraining the femur in a novel statically determinate fashion in combination with using a complex set of muscle forces. In tandem with this, we have shown that not only the deflections but also the stress and strain predictions turn out to be much lower in magnitude, as a result of using the latter approach. To illustrate the dramatic change in results, we compared these results with those of two other models employing commonly used boundary and loading conditions in retrograde stabilization of a distal diaphyseal fracture. The model used herewith resulted in more realistic femoral cortical strains, lower stresses on both the nail and the screws, as well as such deflections in the overall structure. © 2015 IPEM. Published by Elsevier Ltd. All rights reserved.
1. Introduction Although intramedullary nailing has become a standard approach to stabilize fractured bone fragments, failures are still encountered as reported in several studies, emphasizing especially interlocking screw failures due to excessive bending and fatigue [1,2], bone refracture and nail failure [3–6]. With a need for improving these devices, it is imperative that the deflections of the implanted femur, stresses in the nail and screws, and the femoral strains be accurately predicted. The finite element method is the de facto biomechanical modeling standard in orthopedics, and an indispensable tool for predicting in vivo biomechanical behavior. Pre-clinical testing of intramedullary nailing systems by finite element analysis (FEA) is critical to determine stability and performance targets for these devices. While a simplified load case and geometry (e.g. a tube under axial compression) may be justified as a conclusive test method for an intramedullary nail (IM nail), the devices’ actual functional performance depends on many factors such as strain distribution in the cortical bone, stress shielding, and shear movement at the fracture site [7,8]. Therefore, it is important to carry out the study on a model reflecting the physiological loading and boundary
∗
Corresponding author. Tel.: +90 216 5780464; fax: +90 216 5780400. E-mail addresses: [email protected] (R. Bayoglu), [email protected], [email protected] (A.F. Okyar).
restraint conditions in order to address and alleviate these issues early in the design stage. The biomechanical response of a nail implanted femur has been investigated in many FEA studies. In most of these, attention seems to favor the proximal part against the distal. In FEA studies focusing on the proximal part, the distal side was either fixed from the mid-diaphysis [9,10] or from the distal-condylar region [11–16]. Only a limited number of studies used restraint conditions with more care. The restraint conditions at the knee in particular, and the overall femur were considered in Speirs et al. [17]. A free-boundary condition approach based on a consistent self-equilibrating musculoskeletal force system was utilized by various groups [18–20]. In most experimental studies involving mechanical tests of nailimplanted femurs, the distal end was rigidly fixed by some means [7,13,15,21–27]. Over-constraining the distal end and excluding the muscles’ forces resulted in a highly over-estimated deflection at the femoral head, as well as very high stresses and strains in the femur and the implant, diverging from in vivo conditions. In Speirs et al. [17], it was shown that an intact femur constrained in a statically determinate fashion at both ends and loaded by all muscles of the femur produced much lower deflections in agreement with in vivo deflection measurements provided by Taylor et al. [11]. The effects of improved boundary and loading conditions have been further elucidated in [18,19,28]. Based on the lower deflections and bending of the femur, it was argued that employing dominant muscular activity aside from the hip-joint contact force and
http://dx.doi.org/10.1016/j.medengphy.2015.08.007 1350-4533/© 2015 IPEM. Published by Elsevier Ltd. All rights reserved.
Please cite this article as: R. Bayoglu, A.F. Okyar, Implementation of boundary conditions in modeling the femur is critical for the evaluation of distal intramedullary nailing, Medical Engineering and Physics (2015), http://dx.doi.org/10.1016/j.medengphy.2015.08.007
JID: JJBE 2
ARTICLE IN PRESS
[m5G;August 30, 2015;13:54]
R. Bayoglu, A.F. Okyar / Medical Engineering and Physics 000 (2015) 1–8
reducing the degree of restraint (mounting, joint restraint, etc.) yield more physiologically relevant results. Distal femoral fractures are rare, but severe, and mostly reported in young men and elderly women [29]. High incidence rates of septic (13%) and aseptic (14%) non-unions have been reported [30]. This type of fracture is difficult to treat due to a decreased blood supply to the fracture area and a lack of stability in the distal metaphyseal region. Thus, the fracture site stability in this type of fractures is still of special clinical interest. Currently, studies on the influence of boundary conditions on the retrograde stabilization of a distal femoral diaphyseal fracture are lacking. We show that boundary conditions are critical for predicting the mechanical response of bone-implant constructs by comparing the FEA results of three distinct loading and restraint cases. Clinically relevant results such as femoral strains, movement at the fracture site and stresses in the nail and screws were disputed. 2. Materials and methods To facilitate comparison with other FEA studies and avoid subject-specific variations in geometry, the standardized geometry of the third-generation composite femur model available in the public domain through the Biomedical Research Community (http://www.biomedtown.org) was used in this study. Finite element modeling and analysis were performed in ADINA [31]. The magnitude and orientation of the hip-joint and muscle force components were defined with respect to a right-handed coordinate system centered at the hip-joint center, as described in Bergmann et al. [32]. A new generation of a relatively short retrograde IM nail with four interlocking screws (two at the proximal and two at the distal sides) stabilizing a femur was created. The 5 mm osteotomy was located in the distal one-third of the diaphysis. The IM nail and the bone model used in this study are depicted in Fig. 1. To allow for the placement of the nail in the intramedullary canal, drilling and reaming processes inside the cancellous bone were performed by intersection and subtraction operations in the software. The short tubular IM nail had outer and inner diameters of 9.5 mm and 4.5 mm, respectively, and a length of 250 mm. The maximum gap between the IM nail and the intramedullary canal was 0.25 mm. Solid circular interlocking pins of 4.5 mm in diameter were used to connect the bone and the nail. The complete structure consisting of the bone, the nail and interlocking pins has been referred to as the bone-nail construct, or simply as the construct.
Fig. 1. Simplified model of the IM nail (left) and the third-generation composite femur (right).
2.1. Boundary and loading conditions We compared three distinct boundary and loading conditions; two of which (cases a and b) corresponded to models used in the majority of similar studies, where the femur was fully constrained at the distal condyles. Only hip-joint loading was considered in case a (cp. [10,14,33]), while the muscles’ loads were included in cases b and c (cp. [12,13,15,16,27]). In our study, the reduced muscle model by Heller et al. [34] has been adopted. As for boundary conditions, a head constraint was utilized in case c, as described in Speirs et al. [17] and as shown in Fig. 2. Additionally, the knee center O and the most lateral node at the distal femoral epicondyle N were also restrained. The head Q was only allowed to translate along an axis between the head and the knee center (the local xl axis from point Q to O). The knee-joint center O was placed at the insertion of the anterior cruciate ligament, as suggested in Horsman et al. [35]. All translational degrees-of-freedom of the knee center were restricted, leaving it essentially as a spherical joint. Point N was restricted from translating in the antero-posterior (A-P) direction only. Thus, in case c, all the spatial degrees-of-freedom of the construct were constrained, yet it remained statically determinate.
Fig. 2. Boundary and loading conditions considered in this study: case a consists of hip-joint contact force with fixed boundary conditions on the distal condyles. Case b is the same as a, but includes the reduced muscle model (abductor, tensor fascia latae and vastus lateralis) additionally. Case c corresponds to the physiological boundary conditions and the reduced muscle model.
As to the question of what activities should be mimicked during an FEA, Bergmann et al. [32] stated that femoral implants should mainly be tested under walking and stair climbing loads, as these activities result in the most critical loading of the femur. This hypothesis was further supported by Morlock et al. [36], where it was pointed out that walking was the most frequent dynamic activity. As far as the peak activity level during walking was concerned, the instant of highest hip-joint contact reaction during walking (first peak at 18% of the
Please cite this article as: R. Bayoglu, A.F. Okyar, Implementation of boundary conditions in modeling the femur is critical for the evaluation of distal intramedullary nailing, Medical Engineering and Physics (2015), http://dx.doi.org/10.1016/j.medengphy.2015.08.007
ARTICLE IN PRESS
JID: JJBE
[m5G;August 30, 2015;13:54]
R. Bayoglu, A.F. Okyar / Medical Engineering and Physics 000 (2015) 1–8 Table 1 Load profile of the construct at the instant of maximum hip-joint contact force during the walking gait cycle (BW = 860 N) [34,37]. Force (N) Hip-joint contact (case a) Abductor Tensor fascia latae-proximal Tensor fascia latae-distal Vastus lateralis Resultant (cases b and c)
Point Q M M M L
Fx
Fy
Fz
F
−670 499 62 −4 −8
229 −37 −100 6 −159
2067 −744 −114 163 799
2185 896 163 164 815
−121
−61
2172
2176
gait cycle in Bergmann [37]) was simulated. Although, it is not customary to walk in the very early postoperative period of retrograde intramedullary nailing where there is negligible callus formation, we considered this as a worst-case scenario. At the instant of maximum hip-joint contact force during the gait, some muscles showed no or negligible activity [34]. Therefore, only the abductors, tensor fascia latae (proximal and distal parts) and vastus lateralis muscles were considered. This reduced muscle model was shown to be in close approximation to the in vivo condition (with an error less than 7% of the measured hip contact reaction) during walking [34]. In our study, the reduced muscle loading was applied to cases b and c, while in case a, only the hip-joint contact force was applied. The load magnitudes were taken from the Orthoload database [37], and were calculated for a patient of 860 N body weight (BW), as shown in Table 1. Note that the load applied at point M was the resultant of the abductors and tensor fascia latae forces.
3
Table 2 Reaction forces at the supports for all cases, corresponding to the loads in Table 1. All values are given in N. Support location
Fx Fy Fz F
Case a
Case b
Case c
Lower extremity
N
Q
O
668 −228 −2067
119 62 −2172
0 70 0
−147 −32 −14
267 24 −2159
119 62 −2172
2185
2177
70
151
2175
2177
convergence analysis was performed until the error in maximum hip displacements and strain energy was reduced to 3%. 3. Results Since the aim of this study was to show that boundary and loading conditions can cause great variations in the results of FEA, a casebased comparison of the three cases of boundary and loading conditions described in the previous section is presented. 3.1. Reaction forces Reaction forces that arise in the construct during walking (18% of the gait cycle in Bergmann [37]) are listed in Table 2. Here, reaction components for cases a and b corresponded to the summation of contributions from the nodes in the distally fixed region, while those for case c arose at nodes N, Q and O.
2.2. Analysis parameters and the mesh A non-linear static large-displacement FEA with an energy convergence tolerance of 5% has been carried out. Non-linearity of the solution was due to using a large-displacement formulation and to the presence of glued contact between the cortical and cancellous regions as well as contact between parts of the construct [38]. The implementation of more realistic contact conditions as opposed to simply bonding the interfaces results in an increase in the accuracy of finite element models (cp. [39]). Thus, the interlocking pins were tied to the bone simulating thread action, while they were allowed to slide in the nails’ guide holes. Frictional sliding at this interface was accommodated by contact elements using a metal/metal coefficient of 0.23. At the interface between the nail and the cancellous portion in the intramedullary canal, contact elements with a friction coefficient of 0.3 were used, as suggested by Eberle et al. [40]. Initial penetration of contact surfaces was neglected. The contact solution was achieved by the Lagrange-multiplier method. Material properties for the nail and pins corresponded to a titanium alloy (Ti-6Al-4V) with an elastic modulus of 114 GPa, Poisson’s ratio of 0.3 and a yield strength of 870 MPa [40,41]. The cortical and cancellous parts were modeled as homogeneous and isotropic media, having a linearly-elastic stress–strain behavior. The elastic moduli ratio of cortical to cancellous regions was taken as 17:1 GPa. Poisson’s ratios for both portions were taken as 0.3. The ratios of cortical to cancellous moduli from various studies were found to lie in the range 11.3–18 except in Montanini and Filardi [15] where a density based elastic modulus assignment was used. The use of linearly elastic isotropic material model allowed for direct comparison of results with other FEA studies [9,11,15,18–20]. Second-order tetrahedral and hexahedral elements were used in mesh construction. The maximum element edge length for the bone, nail and pins were set as 3, 1.25 and 0.7 mm, respectively. Mesh refinements were applied at critical locations such as guide (screw) holes. The construct was discretized by a total of nearly 106 elements and 6 × 105 nodes. For the current mesh configuration, mesh
3.2. Construct displacements For the three cases, deflected constructs in the anterior (A) and medial (M) views are shown in Fig. 3. The application of the hip contact force alone produced significant bending in the coronal and sagittal planes, resulting in a total displacement magnitude of approximately 168 mm at the femoral head in case a. However, in case b, the addition of muscle forces prevented excessive bending in the sagittal plane caused by the hip contact force alone, where a maximum deflection of 48.4 mm was read. The displacement of the construct decreased significantly by the so-called physiological boundary conditions (from [17]) utilized in case c. The bending action in the coronal plane was much more balanced in comparison to case b. In case c, maximum deflection at the greater trochanteric region was read as 2.3 mm. 3.3. Stress distribution in the implant The equivalent (von Mises) stress distributions within the IM nail are shown for the three cases in Fig. 4. The maximum equivalent stress always occurred at the fracture site where 5730, 2177 and 326 MPa were read for cases a, b and c, respectively. The equivalent stress distributions on the interlocking pins are shown in Fig. 5. The location of maximum stress was marked in all cases. Maximum stress magnitudes for the interlocking pins and nail guide holes are listed in Table 3 for the three cases. In cases b and c, the second proximal guide hole was the most critical among four guide holes, with an equivalent stress of 288 and 254 MPa, respectively, indicating higher load transmission there. However, in case a it was the first distal guide hole with an equivalent stress of 552 MPa. In all cases, the second proximal interlocking pin (Pin 2 in Fig. 2) was the most critical with 460, 210 and 215 MPa for cases a, b and c, respectively. The maximum stresses on the interlocking pins were 210 MPa (proximal) and 194 MPa (distal) in case b, and as 215 MPa (proximal) and 110 MPa (distal) in case c.
Please cite this article as: R. Bayoglu, A.F. Okyar, Implementation of boundary conditions in modeling the femur is critical for the evaluation of distal intramedullary nailing, Medical Engineering and Physics (2015), http://dx.doi.org/10.1016/j.medengphy.2015.08.007
JID: JJBE 4
ARTICLE IN PRESS
[m5G;August 30, 2015;13:54]
R. Bayoglu, A.F. Okyar / Medical Engineering and Physics 000 (2015) 1–8
Fig. 4. von Mises stress distribution on the IM nail surface. Fig. 3. Displacement contours under walking loads in the anterior (first row) and medial (second row) views where the reference configurations are shown in shaded color. Case c was scaled five-fold for clarity. Location of maximum deflection was marked in all cases. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
3.4. Cortical strain distribution Cortical strains were monitored along the anterior, lateral, posterior and medial aspects of the diaphysis. Maximum and minimum principal strain components are shown in Fig. 6. Principal tensile and compressive strains of +7060μ, −6830μ around the second proximal hole and +18960μ, −8270μ at the lateral aspect of the distal fracture surface were read in case a. In case b, principal strains peaks of −4500μ, +4360μ were recorded in the medial and lateral aspects of the second proximal hole, respectively. The bending in the coronal plane was much less pronounced in case b in comparison with case a. Finally in case c, peak principal strains of −1650μ, +1000μ in the inferior neck and lateral sub-trochanteric aspects were recorded. 3.5. Movement at the fracture site For the three cases, the total displacements at the proximal and distal fracture surfaces of the cortical bone are presented in Fig. 7. In addition, axial and shear displacements are shown in Table 4. Maximum displacements of 9.1, 2.4 and 0.4 mm were found at the proximal surfaces for cases a, b and c, respectively. In cases a and b, distal fracture surfaces had much lower displacements compared with the proximal sides. On the contrary, similar magnitudes were read for case c. 4. Discussion The aim of this study was to show that boundary conditions in modeling the femur are critical for the design of IM nails. For this
Fig. 5. von Mises stress distribution on the interlocking pins. Table 3 Maximum von Mises stresses on the nail guide holes and interlocking pins for all cases. 1p and 2p stand for the first and second proximal positions, while 1d and 2d are the corresponding positions on the distal side. Bold text indicates the maximum stressed locations for each case. Cases
a b c
Nail
5730 2180 326
Guide holes
Interlocking pins
1p
2p
1d
2d
1p
2p
1d
2d
465 223 162
505 288 254
552 229 109
287 145 81
439 190 157
460 210 215
377 194 110
235 149 94
purpose, three distinct cases of boundary and loading conditions were tested. The equivalent reaction forces in Table 2 for all cases almost identically balanced the external loads in Table 1. This provided a consistency check of our FEA results. The huge hip displacements reported for cases a and b showed that these models resulted in a loss of mechanical stability of the
Please cite this article as: R. Bayoglu, A.F. Okyar, Implementation of boundary conditions in modeling the femur is critical for the evaluation of distal intramedullary nailing, Medical Engineering and Physics (2015), http://dx.doi.org/10.1016/j.medengphy.2015.08.007
JID: JJBE
ARTICLE IN PRESS
[m5G;August 30, 2015;13:54]
R. Bayoglu, A.F. Okyar / Medical Engineering and Physics 000 (2015) 1–8
5
Fig. 7. Displacement distributions at the proximal and distal fracture surfaces.
Table 4 Maximum displacements in mm at both ends of the fracture site. Proximal segment
Case a Case b Case c
Fig. 6. Main principal strains along the cortex on the medial and lateral sides (above) and anterior and posterior sides (below). Dotted red lines marked with squares and dashed magenta lines marked with circles correspond to cases a and b, respectively, and scaled on the lower x-axis (with higher micro-strain magnitudes). Solid blue lines marked with inverted triangles of case c are scaled on the upper x-axis. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Distal segment
Axial
Shear
Total
Axial
Shear
Total
6.3 2.2 0.4
6.6 0.9 0.0
9.1 2.4 0.4
0.4 0.1 0.3
1.1 0.0 0.0
1.2 0.1 0.3
construct (i.e. buckling of the nail), while in case c stability was conserved. The pronounced nature of deflections in cases a and b were due to the cantilever column effect in these cases compared with the simply supported column in case c. In cantilever type columns, the hip center displaces further away from the bone axis, which in turn causes a larger bending action on the IM nail creating a positive feedback. (This effect is observed only in large-displacement finite element formulations which require a non-linear iteration procedure.) Clearly, unrealistic deflections were produced in cases a and b. In case c, the maximum deflection at the greater trochanteric region was read as 2.3 mm, which was at least empirically more realistic in comparison with cases a and b. The fracture healing process depends on several factors, and in case of non-union, a secondary operation might be necessary [42,43]. Of these factors, local stress and strain magnitudes at the fracture area are critical, as they provide mechanical stimuli for the process. In an experimental study performed on sheep [7], an inter-fragmentary relative shear movement larger than 1.5 mm at the fracture site considerably delayed healing in transverse diaphyseal fractures, while a relative axial motion of similar magnitude improved it. This indicates that shear movement at the fracture site should be taken into account during the design phase of IM nails [30]. The three cases resulted in different shear displacements at the fracture site as seen in Fig. 7 and Table 4. The pronounced shear deflections in cases a and b are due to the over-estimated bending in these cases. Case c produced shear displacements at the fracture site which were reduced by at least an order of magnitude. In a series of studies on the stress and strain distribution within the intact femur [11,18,20,28] it was suggested that mechanism(s) exist which act to minimize bending and produce a predominately compressive stress/strain distribution. The results from cases a and b, in general, are not realistic in this sense. In particular, the shear displacements from both of these cases may be considered as gross over-estimations of the real values. In Kyle [44], the mechanical failure of IM nails has been attributed to two modes: plastic collapse and fatigue fracture. Nail failures have also been reported in Griza and co-workers [4–6]. Griza et al. [4] compared the failure modes of a slotted and an unslotted nail. The
Please cite this article as: R. Bayoglu, A.F. Okyar, Implementation of boundary conditions in modeling the femur is critical for the evaluation of distal intramedullary nailing, Medical Engineering and Physics (2015), http://dx.doi.org/10.1016/j.medengphy.2015.08.007
ARTICLE IN PRESS
JID: JJBE 6
[m5G;August 30, 2015;13:54]
R. Bayoglu, A.F. Okyar / Medical Engineering and Physics 000 (2015) 1–8 Table 5 Comparison of principal strains with various other studies. HJR: hip-joint reaction, Abd.: abductors, Iliotib.: iliotibial band, Iliops: Iliopsoas, VL: vastus lateralis. Modulus ratio: cortical to cancellous elastic modulus ratio. SD: statically determinate. THR: total hip reconstruction. Ref./type
Proximal diaphysis
Neck
Medial
Lateral
Inferior
Case a Case b Case c [45]/in vivo Intact [15]/FEA antegrade nailing
−950μ −2550μ −1410μ
+410μ +1950μ +960μ +1200μ
−1590μ −1820μ −1640μ
[27]/in vitro retrograde nailing
−2800μ
[23]/in vitro Intact
−3800μ
+2200μ
−3700μ −900μ
−1000μ
+600μ
[18]/FEA Intact
−1500μ
+1150μ
[19]/FEA Intact
−700μ
+500μ
−1350μ
+1250μ +2500μ
[20]/FEA Intact [11]/FEA Intact
−1500μ
−1900μ
+2250μ
[28]/in vitro Intact
[9]/FEA THR
Material/loading/constraint
−750μ
−2750μ
+500μ
slotted nail having a lower bending stiffness failed due to plastic collapse. The unslotted nail, similar in geometry to our nail and loaded severely, did not undergo any significant geometry change but failed due to fatigue fracture. Considerably large differences in equivalent stress magnitude and distribution in the nail were found between the three cases, as shown in Fig. 4. The mid-diaphysis section of the nail is clearly under a state of plastic collapse, with von Mises stresses reaching 5730 MPa and 2180 MPa in cases a and b, respectively. Note that the nail material has a yield point of 870 MPa. In case c on the contrary, the most highly stressed locations are around the guide holes in the nail. Maximum equivalent stresses around the guide holes are shown in Table 3. At this level of stress, failure in case c is anticipated as fatigue around the most highly-stressed hole. In a study of mechanical failure in intramedullary interlocking nails [6], 17 nail failures out of 286 femoral nailings were reported. Most of these failures occurred due to mechanical fatigue around the nails’ distal guide holes. This was found to be in accordance with the stress levels of case c. In Table 3, the maximum equivalent stress around the nail guide holes were 552 MPa, 288 MPa, and 254 MPa for cases a, b and c, respectively. Note that all values were below the yield stress. Thus, cases a and b clearly do not reproduce the observed failure mode of the nail. They are simply unrealistic in comparison with case c. Stress contours were also observed along the interlocking pin surfaces, as shown in Fig. 5. In another FEA study about distal femoral fracture stabilization by retrograde IM nailing [16], a maximum equivalent stress of 629 MPa in the proximal and 191 MPa in the distal pins has been reported for the single-leg stance position. Their loading and boundary conditions matched nearly with those of case b. In Table 3, we read for case b a maximum equivalent stress of 210 MPa and 194 MPa for the proximal and distal pins, respectively. In Wu and Shih [3] it was found that the highest risk of failure occurred at the distal holes. All of our cases as well as [16] were short of predicting the location of highest stress and thus failure. They all predicted criticality on the proximal side rather than the distal.
Peak walking load. Linearly elastic isotropic, modulus ratio 10:0. Peak walking load applied via HJR + Abd. + VL Distally fixed. Synthetic. Peak walking load applied via HJR. Distally fixed. Synthetic. Peak walking load applied via HJR + Abd. + Iliotib. + VL Distally fixed. Synthetic. Single leg stance load applied via HJR + Abd + Iliops. + VL Distally fixed and head constrained. Linearly elastic isotropic, modulus ratio 17:1.5. Peak walking load applied via HJR + all thigh muscles. Distally fixed. Linearly elastic isotropic, modulus ratio 17:1.5. Partial walking load applied via HJR + all muscles. SD constraint set at the knee. Density-based elastic modulus. Peak walking load applied via HJR + all thigh muscles. Distally fixed. Linearly elastic isotropic, modulus ratio 18:1. Single leg stance applied via free-boundary condition approach. Linearly elastic isotropic, modulus ratio 17:1. Peak walking load applied via HJR + Abd. + Iliotib. + Iliops. Distally fixed.
The distribution of principal strains on the critical surface provided a means to evaluate the degree of loading of the bone and was of clinical relevance. Principal strain components at various aspects of the bone by a number of references are tabulated in Table 5 for comparison. The locations where strains were most frequently reported included the medial and lateral aspects of the proximal diaphysis and the interior (medial) aspect of the neck. A majority of the studies were FEA. Additionally, there were three studies involving in vitro experiments, and one in vivo study. In all but one of the FEA studies, a linearly elastic and isotropic material model was used. An in vivo peak principal strain of +1200μ at the proximal lateral femoral aspect of a walking patient (weighing approximately 65 kg) was reported in Aamodt et al. [45]. Of our three cases, case c was in best agreement with a peak principal strain of +960μ. Interestingly, our strain reading was 20% lower than the in vivo one despite the use of a heavier patient (weighing 87 kg) in our model. This meant that either the cortical elastic modulus or the cortical shell thickness was under-estimated by our model, resulting in a more compliant response than what would be expected. Two other FEA simulations in Table 5 [18,19] were also in good agreement with the in vivo strain. (Note that the reduced strain of [19] was a result of partial loading of that model.) In both, all the rigid-body degrees-of-freedom of the femur were eliminated, although a head constraint was not utilized. In addition, a consistent self-equilibrating loading scheme including all thigh muscles was used. In contrast, we have used only the hip-joint reaction and dominant muscular action in the proximal aspect in case c which was still in good agreement with [45]. The strains in cases a and b were unrealistically high. Thus, distally fixing the entire femur and/or not including the active muscles produced erroneous strains. Although the knee joint essentially has six degrees of freedom, its movement is restrained in many directions due to its complex ligamentous structure. For example, anterior and posterior cruciate ligaments constrain A-P translation of the knee [46]. Of the soft tissues
Please cite this article as: R. Bayoglu, A.F. Okyar, Implementation of boundary conditions in modeling the femur is critical for the evaluation of distal intramedullary nailing, Medical Engineering and Physics (2015), http://dx.doi.org/10.1016/j.medengphy.2015.08.007
JID: JJBE
ARTICLE IN PRESS
[m5G;August 30, 2015;13:54]
R. Bayoglu, A.F. Okyar / Medical Engineering and Physics 000 (2015) 1–8
that attach to the lateral side of the femur, the popliteus muscle– tendon unit originates from lateral femoral epicondyle and restrains anterior translation [46] and popliteofibular and lateral collateral ligaments restrain posterior translation [47,48]. Point N at the distal lateral epicondyle corresponded approximately to a location between the popliteus muscles’ and lateral collateral ligaments’ attachment sites. In case c, this point was constrained in the A-P direction to represent the function of these ligaments. Instead of over-constraining the femur by fixing the distal part entirely, as in cases a and b, using the set of boundary conditions in case c provided empirically realistic results. Including all muscles in an experimental set-up or a finite element environment is a complex process, making the controllability and reproducibility of these tests difficult. Results showed that case c produced plausible levels of deflection, nail stress and cortical strain. Moreover, the relative motion at the fracture site was significantly lower in comparison with the other cases. The mode of nail failure was also correctly predicted. From an engineering point of view, we conclude that the application of dominant muscular actions in addition to restraining the head, the knee and the distal lateral epicondyle, as shown in Speirs et al. [17], was an effective way to carry out a physiologically more realistic FEA compared with models that did not do so. Conflict of interest None declared. Funding The research was conducted in the Biomechanics Research Laboratory located in the Faculty of Engineering at the Yeditepe University. The software and hardware used for the purposes of conducting this research was paid for by the Research and Development Office of the Yeditepe University. Ethical approval Not required. References [1] Boenisch UW, de Boer PG, Journeaux SF. Unreamed intramedullary tibial nailing– fatigue of locking bolts. Injury 1996;27(4):265–70. [2] Kneifel T, Buckley R. A comparison of one versus two distal locking screws in tibial fractures treated with unreamed tibial nails: a prospective randomized clinical trial. Injury 1996;27(4):271–3. [3] Wu C-C, Shih C-H. Biomechanical analysis of the mechanism of interlocking nail failure. Arch Orthop Traum Su 1992;111(5):268–72. doi:10.1007/BF00571522. [4] Griza S, Zimmer CG, Reguly A, Strohaecker TR. A case study of subsequential intramedullary nails failure. Eng Failure Anal 2009;16(3):728–32. [5] Zimmerman KW, Klasen HJ. Mechanical failure of intramedullary nails after fracture union. J Bone Joint Surg Br 1983;65-B(3):274–5. [6] Bhat AK, Rao SK, Bhaskaranand K. Mechanical failure in intramedullary interlocking nails. J Orthop Surg (Hong Kong) 2006;14(2):138–41. [7] Augat P, Burger J, Schorlemmer S, Henke T, Peraus M, Claes L. Shear movement at the fracture site delays healing in a diaphyseal fracture model. J Orthop Res 2003;21(6):1011–17. doi:10.1016/S0736-0266(03)00098-6. [8] Duda GN, Kirchner H, Wilke H-J, Claes L. A method to determine the 3-d stiffness of fracture fixation devices and its application to predict inter-fragmentary movement. J Biomech 1997;31(3):247–52. [9] Stolk J, Verdonschot N, Huiskes R. Hip-joint and abductor-muscle forces adequately represent in vivo loading of a cemented total hip reconstruction. J Biomech 2001;34(7):917–26. http://dx.doi.org/10.1016/S0021-9290(00)002256. http://www.sciencedirect.com/science/article/pii/S0021929000002256. [10] Tupis TM, Altman GT, Altman DT, Cook HA, Miller MC. Femoral bone strains during antegrade nailing: a comparison of two entry points with identical nails using finite element analysis. Clin Biomech 2012;27(4):354–9. http://dx.doi.org/ 10.1016/j.clinbiomech.2011.11.002. http://www.sciencedirect.com/science/article/ pii/S0268003311002907. [11] Taylor ME, Tanner KE, Freeman MAR, Yettram AL. Stress and strain distribution within the intact femur: compression or bending? Med Eng Phys 1996;18(2):122– 31.
7
[12] Papathanasopoulou V, Fotiadis D, Massalas C. Intact and implanted femur behaviour during walking and jogging. In: Engineering in medicine and biology society, 2001. Proceedings of the 23rd annual international conference of the IEEE, 2. IEEE; 2001. p. 1524–7. [13] Cheung G, Zalzal P, Bhandari M, Spelt JK, Papini M. Finite element analysis of a femoral retrograde intramedullary nail subject to gait loading. Med Eng Phys 2004;26(2):93–108. [14] Kajzer W, Kajzer A, Marciniak J. Fem analysis of expandable intramedullary nails in healthy and osteoporotic femur. J Achievements Mater Manufac Eng 2009;37(2):563–70. [15] Montanini R, Filardi V. In vitro biomechanical evaluation of antegrade femoral nailing at early and late postoperative stages. Med Eng Phys 2010;32(8):889–97. [16] Shih K-S, Hsu C-C, Hsu T-P, Hou S-M, Liaw C-K. Biomechanical analyses of static and dynamic fixation techniques of retrograde interlocking femoral nailing using nonlinear finite element methods. Comput Meth Prog Biomed 2014; 113(2):456–64. doi:10.1016/j.cmpb.2013.11.002. [17] Speirs AD, Heller MO, Duda GN, Taylor WR. Physiologically based boundary conditions in finite element modelling. J Biomech 2007;40(10):2318–23. [18] Duda GN, Heller M, Albinger J, Schulz O, Schneider E, Claes L. Influence of muscle forces on femoral strain distribution. J Biomech 1998;31(9):841–6. [19] Polgar K, Gill HS, Viceconti M, Murray DW, O’Connor JJ. Strain distribution within the human femur due to physiological and simplified loading: finite element analysis using the muscle standardized femur model. Proc Inst Mech Eng H 2003;217(3):173–89. [20] Phillips ATM. The femur as a musculo-skeletal construct: A free boundary condition modelling approach. Med Eng Phys 2009;31(6):673–80. [21] George CJ, Lindsey RW, Noble PC, Alexander JW, Kamaric E. Optimal location of a single distal interlocking screw in intramedullary nailing of distal third femoral shaft fractures. J Orthop Traum 1998;12(4):267–72. [22] Schandelmaier P, Farouk O, Krettek C, Reimers N, Mannss J, Tscherne H. Biomechanics of femoral interlocking nails. Injury 2000;31(6):437–43. [23] Szivek JA, Benjamin JB, Anderson PL. An experimental method for the application of lateral muscle loading and its effect on femoral strain distributions. Med Eng Phys 2000;22(2):109–16. [24] Schneider E, Michel MC, Genge M, Zuber K, Ganz R, Perren SM. Loads acting in an intramedullary nail during fracture healing in the human femur. J Biomech 2001;34(7):849–57. [25] Wang G, Pan T, Peng X, Wang J. A new intramedullary nailing device for the treatment of femoral shaft fractures: a biomechanical study. Clin Biomech 2008;23(3):305–12. [26] Kajzer W, Kajzer A, Marciniak J. Expandable intramedullary nail – experimental biomechanical evaluation. Arch Mater Sci Eng 2010;41(1):45–52. [27] Hak DJ, Neiman R, Hazelwood S. Biomechanical strain analysis of the proximal femur following retrograde intramedullary nailing. Curr Orthop Pract 2010;21(4):385–9. http://dx.doi.org/10.1097/BCO.0b013e3181d73bae. [28] Simoes JA, Vaz MA, Blatcher S, Taylor M. Influence of head constraint and muscle forces on the strain distribution within the intact femur. Med Eng Phys 2000;22(7):453–9. [29] Court-Brown CM, Caeser B. Epidemiology of adult fractures: A review. Injury 2006;37:691–7. doi:10.1016/j.injury.2006.04.130. [30] Ehlinger M, Ducrot G, Adam P, Bonnomet F. Distal femur fractures. surgical techniques and a review of the literature. Orthop Traum Surg Res 2013;99(3):353– 60. http://dx.doi.org/10.1016/j.otsr.2012.10.014. http://www.sciencedirect.com/ science/article/pii/S1877056813000200. [31] ADINA R&D, Inc. Release 8.9, Watertown, MA, USA; 2013. [32] Bergmann G, Deuretzbacher G, Heller M, Graichen F, Rohlmann A, Strauss J, et al. Hip contact forces and gait patterns from routine activities. J Biomech 2001;34:859–71. [33] Chen SH, Yu TC, Chang CH, Lu YC. Biomechanical analysis of retrograde intramedullary nail fixation in distal femoral fractures. The Knee 2008;15(5):384–9. [34] Heller MO, Bergmann G, Kassi JP, Claes L, Haas NP, Duda GN. Determination of muscle loading at the hip joint for use in pre-clinical testing. J Biomech 2005;38(5):1155–63. [35] Horsman MDK, Koopman HFJM, van der Helm FCT, Pros LP, Veeger HEJ. Morphological muscle and joint parameters for musculoskeletal modelling of the lower extremity. Clin Biomech 2007;22(2):239–47. http://dx.doi.org/10.1016/ j.clinbiomech.2006.10.003. http://www.sciencedirect.com/science/article/pii/ S0268003306001896. [36] Morlock M, Schneider E, Bluhm A, Vollmer M, Bergmann G, Muller V, et al. Duration and frequency of every day activities in total hip patients. J Biomech 2001;34(7):873–81. [37] Bergmann G., editor, 2002. HIP98 – Loading of the hip joint. Free University, Berlin, ISBN 3-9807848-0-0; 1998. [38] Bayoglu R, Okyar AF. A physiologically accurate mechanical representation of the bone-implant construct under gait loads. In: Proceedings of the sixth national biomechanics congress, Sakarya University, SAUFBE, vol. 16 (3); 2012. p. 136–43. [39] Grant C. Mechanical testing and modelling of a bone-implant construct: contemporary methods and analysis. Queensland University of Technology; 2012. PhD Thesis. Brisbane, Australia. [40] Eberle S, Gerber C, von Eldenburg G, Hungerer S, Augat P. Type of hip fracture determines load share in intramedullary osteosynthesis. Clin Orthop Relat Res 2009;497(8):1972–80. [41] Material Property Data; (2014). URL http://www.matweb.com. [42] McKibbin B. The biology of fracture healing in long bones. J Bone Joint Surg Br 1978;60-B(2):150–62. http://www.bjj.boneandjoint.org.uk/content/60B/2/150.full.pdf. http://www.bjj.boneandjoint.org.uk/content/60-B/2/150.short.
Please cite this article as: R. Bayoglu, A.F. Okyar, Implementation of boundary conditions in modeling the femur is critical for the evaluation of distal intramedullary nailing, Medical Engineering and Physics (2015), http://dx.doi.org/10.1016/j.medengphy.2015.08.007
JID: JJBE 8
ARTICLE IN PRESS
[m5G;August 30, 2015;13:54]
R. Bayoglu, A.F. Okyar / Medical Engineering and Physics 000 (2015) 1–8
[43] Rodriguez EK, Boulton C, Weaver MJ, Herder LM, Chacko JHMAT, Appleton PT, et al. Predictive factors of distal femoral fracture nonunion after lateral locked plating: a retrospective multicenter case-control study of 283 fractures. Injury 2014;45(3):554–9. doi:10.1016/j.injury.2013.10.042. [44] Kyle R. Biomechanics of intramedullary fracture fixation. Orthopedics 1985;8(11):13561359. http://europepmc.org/abstract/MED/3832024. [45] Aamodt A, Lund-Larsen J, Eine J, Andersen E, Benum P, Husby OS. In vivo measurements show tensile axial strain in the proximal lateral aspect of the human femur. J Orthop Res 1997;15:927–31. [46] Halewood C, Amis A. Clinically relevant biomechanics of the knee capsule and ligaments. Knee Surg Sports Traumatol Arthrosc 2015. doi:10.1007/s00167-0153594-8.
[47] Veltri DM, Deng X-H, Torzilli PA, Warren RF, Maynard MJ. The role of the cruciate and posterolateral ligaments in stability of the knee: a biomechanical study. Am J Sport Med 1995;23(4):436–43. http://ajs.sagepub.com/content/23/4/436. full.pdf. doi:10.1177/036354659502300411. http://ajs.sagepub.com/content/23/ 4/436.abstract. [48] Shahane SA, Ibbotson C, Strachan R, Bickerstaff D. The popliteofibular ligament: An anatomical study of the posterolateral corner of the knee. J Bone Joint Surg Br 1999;81-B(4):636–42. http://www.bjj.boneandjoint.org.uk/content/81-B/4/636. full.pdf. http://www.bjj.boneandjoint.org.uk/content/81-B/4/636.abstract.
Please cite this article as: R. Bayoglu, A.F. Okyar, Implementation of boundary conditions in modeling the femur is critical for the evaluation of distal intramedullary nailing, Medical Engineering and Physics (2015), http://dx.doi.org/10.1016/j.medengphy.2015.08.007
JID: JJBE
[m5G;August 30, 2015;13:54]
Medical Engineering and Physics 000 (2015) 1–8
Contents lists available at ScienceDirect
Medical Engineering and Physics journal homepage: www.elsevier.com/locate/medengphy
Implementation of boundary conditions in modeling the femur is critical for the evaluation of distal intramedullary nailing Riza Bayoglu, A. Fethi Okyar∗ Department of Mechanical Engineering, Yeditepe University, Atasehir, Istanbul 34755, Turkey
a r t i c l e
i n f o
Article history: Received 24 January 2014 Revised 8 August 2015 Accepted 12 August 2015 Available online xxx Keywords: Intramedullary nail Retrograde stabilization Pre-clinical testing Distal femoral fracture Physiological boundary conditions Finite element method
a b s t r a c t In previous numerical and experimental studies of the intramedullary nail-implanted human femur several simplifications to model the boundary and loading conditions during pre-clinical testing have been proposed. The distal end of the femur was fixed in the majority of studies dealing with the biomechanics of the lower extremity, be it numerical or experimental, which resulted in obviously non-physiological deflections. Per contra, Speirs et al. (2007) proclaimed physiological deflections as a result of constraining the femur in a novel statically determinate fashion in combination with using a complex set of muscle forces. In tandem with this, we have shown that not only the deflections but also the stress and strain predictions turn out to be much lower in magnitude, as a result of using the latter approach. To illustrate the dramatic change in results, we compared these results with those of two other models employing commonly used boundary and loading conditions in retrograde stabilization of a distal diaphyseal fracture. The model used herewith resulted in more realistic femoral cortical strains, lower stresses on both the nail and the screws, as well as such deflections in the overall structure. © 2015 IPEM. Published by Elsevier Ltd. All rights reserved.
1. Introduction Although intramedullary nailing has become a standard approach to stabilize fractured bone fragments, failures are still encountered as reported in several studies, emphasizing especially interlocking screw failures due to excessive bending and fatigue [1,2], bone refracture and nail failure [3–6]. With a need for improving these devices, it is imperative that the deflections of the implanted femur, stresses in the nail and screws, and the femoral strains be accurately predicted. The finite element method is the de facto biomechanical modeling standard in orthopedics, and an indispensable tool for predicting in vivo biomechanical behavior. Pre-clinical testing of intramedullary nailing systems by finite element analysis (FEA) is critical to determine stability and performance targets for these devices. While a simplified load case and geometry (e.g. a tube under axial compression) may be justified as a conclusive test method for an intramedullary nail (IM nail), the devices’ actual functional performance depends on many factors such as strain distribution in the cortical bone, stress shielding, and shear movement at the fracture site [7,8]. Therefore, it is important to carry out the study on a model reflecting the physiological loading and boundary
∗
Corresponding author. Tel.: +90 216 5780464; fax: +90 216 5780400. E-mail addresses: [email protected] (R. Bayoglu), [email protected], [email protected] (A.F. Okyar).
restraint conditions in order to address and alleviate these issues early in the design stage. The biomechanical response of a nail implanted femur has been investigated in many FEA studies. In most of these, attention seems to favor the proximal part against the distal. In FEA studies focusing on the proximal part, the distal side was either fixed from the mid-diaphysis [9,10] or from the distal-condylar region [11–16]. Only a limited number of studies used restraint conditions with more care. The restraint conditions at the knee in particular, and the overall femur were considered in Speirs et al. [17]. A free-boundary condition approach based on a consistent self-equilibrating musculoskeletal force system was utilized by various groups [18–20]. In most experimental studies involving mechanical tests of nailimplanted femurs, the distal end was rigidly fixed by some means [7,13,15,21–27]. Over-constraining the distal end and excluding the muscles’ forces resulted in a highly over-estimated deflection at the femoral head, as well as very high stresses and strains in the femur and the implant, diverging from in vivo conditions. In Speirs et al. [17], it was shown that an intact femur constrained in a statically determinate fashion at both ends and loaded by all muscles of the femur produced much lower deflections in agreement with in vivo deflection measurements provided by Taylor et al. [11]. The effects of improved boundary and loading conditions have been further elucidated in [18,19,28]. Based on the lower deflections and bending of the femur, it was argued that employing dominant muscular activity aside from the hip-joint contact force and
http://dx.doi.org/10.1016/j.medengphy.2015.08.007 1350-4533/© 2015 IPEM. Published by Elsevier Ltd. All rights reserved.
Please cite this article as: R. Bayoglu, A.F. Okyar, Implementation of boundary conditions in modeling the femur is critical for the evaluation of distal intramedullary nailing, Medical Engineering and Physics (2015), http://dx.doi.org/10.1016/j.medengphy.2015.08.007
JID: JJBE 2
ARTICLE IN PRESS
[m5G;August 30, 2015;13:54]
R. Bayoglu, A.F. Okyar / Medical Engineering and Physics 000 (2015) 1–8
reducing the degree of restraint (mounting, joint restraint, etc.) yield more physiologically relevant results. Distal femoral fractures are rare, but severe, and mostly reported in young men and elderly women [29]. High incidence rates of septic (13%) and aseptic (14%) non-unions have been reported [30]. This type of fracture is difficult to treat due to a decreased blood supply to the fracture area and a lack of stability in the distal metaphyseal region. Thus, the fracture site stability in this type of fractures is still of special clinical interest. Currently, studies on the influence of boundary conditions on the retrograde stabilization of a distal femoral diaphyseal fracture are lacking. We show that boundary conditions are critical for predicting the mechanical response of bone-implant constructs by comparing the FEA results of three distinct loading and restraint cases. Clinically relevant results such as femoral strains, movement at the fracture site and stresses in the nail and screws were disputed. 2. Materials and methods To facilitate comparison with other FEA studies and avoid subject-specific variations in geometry, the standardized geometry of the third-generation composite femur model available in the public domain through the Biomedical Research Community (http://www.biomedtown.org) was used in this study. Finite element modeling and analysis were performed in ADINA [31]. The magnitude and orientation of the hip-joint and muscle force components were defined with respect to a right-handed coordinate system centered at the hip-joint center, as described in Bergmann et al. [32]. A new generation of a relatively short retrograde IM nail with four interlocking screws (two at the proximal and two at the distal sides) stabilizing a femur was created. The 5 mm osteotomy was located in the distal one-third of the diaphysis. The IM nail and the bone model used in this study are depicted in Fig. 1. To allow for the placement of the nail in the intramedullary canal, drilling and reaming processes inside the cancellous bone were performed by intersection and subtraction operations in the software. The short tubular IM nail had outer and inner diameters of 9.5 mm and 4.5 mm, respectively, and a length of 250 mm. The maximum gap between the IM nail and the intramedullary canal was 0.25 mm. Solid circular interlocking pins of 4.5 mm in diameter were used to connect the bone and the nail. The complete structure consisting of the bone, the nail and interlocking pins has been referred to as the bone-nail construct, or simply as the construct.
Fig. 1. Simplified model of the IM nail (left) and the third-generation composite femur (right).
2.1. Boundary and loading conditions We compared three distinct boundary and loading conditions; two of which (cases a and b) corresponded to models used in the majority of similar studies, where the femur was fully constrained at the distal condyles. Only hip-joint loading was considered in case a (cp. [10,14,33]), while the muscles’ loads were included in cases b and c (cp. [12,13,15,16,27]). In our study, the reduced muscle model by Heller et al. [34] has been adopted. As for boundary conditions, a head constraint was utilized in case c, as described in Speirs et al. [17] and as shown in Fig. 2. Additionally, the knee center O and the most lateral node at the distal femoral epicondyle N were also restrained. The head Q was only allowed to translate along an axis between the head and the knee center (the local xl axis from point Q to O). The knee-joint center O was placed at the insertion of the anterior cruciate ligament, as suggested in Horsman et al. [35]. All translational degrees-of-freedom of the knee center were restricted, leaving it essentially as a spherical joint. Point N was restricted from translating in the antero-posterior (A-P) direction only. Thus, in case c, all the spatial degrees-of-freedom of the construct were constrained, yet it remained statically determinate.
Fig. 2. Boundary and loading conditions considered in this study: case a consists of hip-joint contact force with fixed boundary conditions on the distal condyles. Case b is the same as a, but includes the reduced muscle model (abductor, tensor fascia latae and vastus lateralis) additionally. Case c corresponds to the physiological boundary conditions and the reduced muscle model.
As to the question of what activities should be mimicked during an FEA, Bergmann et al. [32] stated that femoral implants should mainly be tested under walking and stair climbing loads, as these activities result in the most critical loading of the femur. This hypothesis was further supported by Morlock et al. [36], where it was pointed out that walking was the most frequent dynamic activity. As far as the peak activity level during walking was concerned, the instant of highest hip-joint contact reaction during walking (first peak at 18% of the
Please cite this article as: R. Bayoglu, A.F. Okyar, Implementation of boundary conditions in modeling the femur is critical for the evaluation of distal intramedullary nailing, Medical Engineering and Physics (2015), http://dx.doi.org/10.1016/j.medengphy.2015.08.007
ARTICLE IN PRESS
JID: JJBE
[m5G;August 30, 2015;13:54]
R. Bayoglu, A.F. Okyar / Medical Engineering and Physics 000 (2015) 1–8 Table 1 Load profile of the construct at the instant of maximum hip-joint contact force during the walking gait cycle (BW = 860 N) [34,37]. Force (N) Hip-joint contact (case a) Abductor Tensor fascia latae-proximal Tensor fascia latae-distal Vastus lateralis Resultant (cases b and c)
Point Q M M M L
Fx
Fy
Fz
F
−670 499 62 −4 −8
229 −37 −100 6 −159
2067 −744 −114 163 799
2185 896 163 164 815
−121
−61
2172
2176
gait cycle in Bergmann [37]) was simulated. Although, it is not customary to walk in the very early postoperative period of retrograde intramedullary nailing where there is negligible callus formation, we considered this as a worst-case scenario. At the instant of maximum hip-joint contact force during the gait, some muscles showed no or negligible activity [34]. Therefore, only the abductors, tensor fascia latae (proximal and distal parts) and vastus lateralis muscles were considered. This reduced muscle model was shown to be in close approximation to the in vivo condition (with an error less than 7% of the measured hip contact reaction) during walking [34]. In our study, the reduced muscle loading was applied to cases b and c, while in case a, only the hip-joint contact force was applied. The load magnitudes were taken from the Orthoload database [37], and were calculated for a patient of 860 N body weight (BW), as shown in Table 1. Note that the load applied at point M was the resultant of the abductors and tensor fascia latae forces.
3
Table 2 Reaction forces at the supports for all cases, corresponding to the loads in Table 1. All values are given in N. Support location
Fx Fy Fz F
Case a
Case b
Case c
Lower extremity
N
Q
O
668 −228 −2067
119 62 −2172
0 70 0
−147 −32 −14
267 24 −2159
119 62 −2172
2185
2177
70
151
2175
2177
convergence analysis was performed until the error in maximum hip displacements and strain energy was reduced to 3%. 3. Results Since the aim of this study was to show that boundary and loading conditions can cause great variations in the results of FEA, a casebased comparison of the three cases of boundary and loading conditions described in the previous section is presented. 3.1. Reaction forces Reaction forces that arise in the construct during walking (18% of the gait cycle in Bergmann [37]) are listed in Table 2. Here, reaction components for cases a and b corresponded to the summation of contributions from the nodes in the distally fixed region, while those for case c arose at nodes N, Q and O.
2.2. Analysis parameters and the mesh A non-linear static large-displacement FEA with an energy convergence tolerance of 5% has been carried out. Non-linearity of the solution was due to using a large-displacement formulation and to the presence of glued contact between the cortical and cancellous regions as well as contact between parts of the construct [38]. The implementation of more realistic contact conditions as opposed to simply bonding the interfaces results in an increase in the accuracy of finite element models (cp. [39]). Thus, the interlocking pins were tied to the bone simulating thread action, while they were allowed to slide in the nails’ guide holes. Frictional sliding at this interface was accommodated by contact elements using a metal/metal coefficient of 0.23. At the interface between the nail and the cancellous portion in the intramedullary canal, contact elements with a friction coefficient of 0.3 were used, as suggested by Eberle et al. [40]. Initial penetration of contact surfaces was neglected. The contact solution was achieved by the Lagrange-multiplier method. Material properties for the nail and pins corresponded to a titanium alloy (Ti-6Al-4V) with an elastic modulus of 114 GPa, Poisson’s ratio of 0.3 and a yield strength of 870 MPa [40,41]. The cortical and cancellous parts were modeled as homogeneous and isotropic media, having a linearly-elastic stress–strain behavior. The elastic moduli ratio of cortical to cancellous regions was taken as 17:1 GPa. Poisson’s ratios for both portions were taken as 0.3. The ratios of cortical to cancellous moduli from various studies were found to lie in the range 11.3–18 except in Montanini and Filardi [15] where a density based elastic modulus assignment was used. The use of linearly elastic isotropic material model allowed for direct comparison of results with other FEA studies [9,11,15,18–20]. Second-order tetrahedral and hexahedral elements were used in mesh construction. The maximum element edge length for the bone, nail and pins were set as 3, 1.25 and 0.7 mm, respectively. Mesh refinements were applied at critical locations such as guide (screw) holes. The construct was discretized by a total of nearly 106 elements and 6 × 105 nodes. For the current mesh configuration, mesh
3.2. Construct displacements For the three cases, deflected constructs in the anterior (A) and medial (M) views are shown in Fig. 3. The application of the hip contact force alone produced significant bending in the coronal and sagittal planes, resulting in a total displacement magnitude of approximately 168 mm at the femoral head in case a. However, in case b, the addition of muscle forces prevented excessive bending in the sagittal plane caused by the hip contact force alone, where a maximum deflection of 48.4 mm was read. The displacement of the construct decreased significantly by the so-called physiological boundary conditions (from [17]) utilized in case c. The bending action in the coronal plane was much more balanced in comparison to case b. In case c, maximum deflection at the greater trochanteric region was read as 2.3 mm. 3.3. Stress distribution in the implant The equivalent (von Mises) stress distributions within the IM nail are shown for the three cases in Fig. 4. The maximum equivalent stress always occurred at the fracture site where 5730, 2177 and 326 MPa were read for cases a, b and c, respectively. The equivalent stress distributions on the interlocking pins are shown in Fig. 5. The location of maximum stress was marked in all cases. Maximum stress magnitudes for the interlocking pins and nail guide holes are listed in Table 3 for the three cases. In cases b and c, the second proximal guide hole was the most critical among four guide holes, with an equivalent stress of 288 and 254 MPa, respectively, indicating higher load transmission there. However, in case a it was the first distal guide hole with an equivalent stress of 552 MPa. In all cases, the second proximal interlocking pin (Pin 2 in Fig. 2) was the most critical with 460, 210 and 215 MPa for cases a, b and c, respectively. The maximum stresses on the interlocking pins were 210 MPa (proximal) and 194 MPa (distal) in case b, and as 215 MPa (proximal) and 110 MPa (distal) in case c.
Please cite this article as: R. Bayoglu, A.F. Okyar, Implementation of boundary conditions in modeling the femur is critical for the evaluation of distal intramedullary nailing, Medical Engineering and Physics (2015), http://dx.doi.org/10.1016/j.medengphy.2015.08.007
JID: JJBE 4
ARTICLE IN PRESS
[m5G;August 30, 2015;13:54]
R. Bayoglu, A.F. Okyar / Medical Engineering and Physics 000 (2015) 1–8
Fig. 4. von Mises stress distribution on the IM nail surface. Fig. 3. Displacement contours under walking loads in the anterior (first row) and medial (second row) views where the reference configurations are shown in shaded color. Case c was scaled five-fold for clarity. Location of maximum deflection was marked in all cases. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
3.4. Cortical strain distribution Cortical strains were monitored along the anterior, lateral, posterior and medial aspects of the diaphysis. Maximum and minimum principal strain components are shown in Fig. 6. Principal tensile and compressive strains of +7060μ, −6830μ around the second proximal hole and +18960μ, −8270μ at the lateral aspect of the distal fracture surface were read in case a. In case b, principal strains peaks of −4500μ, +4360μ were recorded in the medial and lateral aspects of the second proximal hole, respectively. The bending in the coronal plane was much less pronounced in case b in comparison with case a. Finally in case c, peak principal strains of −1650μ, +1000μ in the inferior neck and lateral sub-trochanteric aspects were recorded. 3.5. Movement at the fracture site For the three cases, the total displacements at the proximal and distal fracture surfaces of the cortical bone are presented in Fig. 7. In addition, axial and shear displacements are shown in Table 4. Maximum displacements of 9.1, 2.4 and 0.4 mm were found at the proximal surfaces for cases a, b and c, respectively. In cases a and b, distal fracture surfaces had much lower displacements compared with the proximal sides. On the contrary, similar magnitudes were read for case c. 4. Discussion The aim of this study was to show that boundary conditions in modeling the femur are critical for the design of IM nails. For this
Fig. 5. von Mises stress distribution on the interlocking pins. Table 3 Maximum von Mises stresses on the nail guide holes and interlocking pins for all cases. 1p and 2p stand for the first and second proximal positions, while 1d and 2d are the corresponding positions on the distal side. Bold text indicates the maximum stressed locations for each case. Cases
a b c
Nail
5730 2180 326
Guide holes
Interlocking pins
1p
2p
1d
2d
1p
2p
1d
2d
465 223 162
505 288 254
552 229 109
287 145 81
439 190 157
460 210 215
377 194 110
235 149 94
purpose, three distinct cases of boundary and loading conditions were tested. The equivalent reaction forces in Table 2 for all cases almost identically balanced the external loads in Table 1. This provided a consistency check of our FEA results. The huge hip displacements reported for cases a and b showed that these models resulted in a loss of mechanical stability of the
Please cite this article as: R. Bayoglu, A.F. Okyar, Implementation of boundary conditions in modeling the femur is critical for the evaluation of distal intramedullary nailing, Medical Engineering and Physics (2015), http://dx.doi.org/10.1016/j.medengphy.2015.08.007
JID: JJBE
ARTICLE IN PRESS
[m5G;August 30, 2015;13:54]
R. Bayoglu, A.F. Okyar / Medical Engineering and Physics 000 (2015) 1–8
5
Fig. 7. Displacement distributions at the proximal and distal fracture surfaces.
Table 4 Maximum displacements in mm at both ends of the fracture site. Proximal segment
Case a Case b Case c
Fig. 6. Main principal strains along the cortex on the medial and lateral sides (above) and anterior and posterior sides (below). Dotted red lines marked with squares and dashed magenta lines marked with circles correspond to cases a and b, respectively, and scaled on the lower x-axis (with higher micro-strain magnitudes). Solid blue lines marked with inverted triangles of case c are scaled on the upper x-axis. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Distal segment
Axial
Shear
Total
Axial
Shear
Total
6.3 2.2 0.4
6.6 0.9 0.0
9.1 2.4 0.4
0.4 0.1 0.3
1.1 0.0 0.0
1.2 0.1 0.3
construct (i.e. buckling of the nail), while in case c stability was conserved. The pronounced nature of deflections in cases a and b were due to the cantilever column effect in these cases compared with the simply supported column in case c. In cantilever type columns, the hip center displaces further away from the bone axis, which in turn causes a larger bending action on the IM nail creating a positive feedback. (This effect is observed only in large-displacement finite element formulations which require a non-linear iteration procedure.) Clearly, unrealistic deflections were produced in cases a and b. In case c, the maximum deflection at the greater trochanteric region was read as 2.3 mm, which was at least empirically more realistic in comparison with cases a and b. The fracture healing process depends on several factors, and in case of non-union, a secondary operation might be necessary [42,43]. Of these factors, local stress and strain magnitudes at the fracture area are critical, as they provide mechanical stimuli for the process. In an experimental study performed on sheep [7], an inter-fragmentary relative shear movement larger than 1.5 mm at the fracture site considerably delayed healing in transverse diaphyseal fractures, while a relative axial motion of similar magnitude improved it. This indicates that shear movement at the fracture site should be taken into account during the design phase of IM nails [30]. The three cases resulted in different shear displacements at the fracture site as seen in Fig. 7 and Table 4. The pronounced shear deflections in cases a and b are due to the over-estimated bending in these cases. Case c produced shear displacements at the fracture site which were reduced by at least an order of magnitude. In a series of studies on the stress and strain distribution within the intact femur [11,18,20,28] it was suggested that mechanism(s) exist which act to minimize bending and produce a predominately compressive stress/strain distribution. The results from cases a and b, in general, are not realistic in this sense. In particular, the shear displacements from both of these cases may be considered as gross over-estimations of the real values. In Kyle [44], the mechanical failure of IM nails has been attributed to two modes: plastic collapse and fatigue fracture. Nail failures have also been reported in Griza and co-workers [4–6]. Griza et al. [4] compared the failure modes of a slotted and an unslotted nail. The
Please cite this article as: R. Bayoglu, A.F. Okyar, Implementation of boundary conditions in modeling the femur is critical for the evaluation of distal intramedullary nailing, Medical Engineering and Physics (2015), http://dx.doi.org/10.1016/j.medengphy.2015.08.007
ARTICLE IN PRESS
JID: JJBE 6
[m5G;August 30, 2015;13:54]
R. Bayoglu, A.F. Okyar / Medical Engineering and Physics 000 (2015) 1–8 Table 5 Comparison of principal strains with various other studies. HJR: hip-joint reaction, Abd.: abductors, Iliotib.: iliotibial band, Iliops: Iliopsoas, VL: vastus lateralis. Modulus ratio: cortical to cancellous elastic modulus ratio. SD: statically determinate. THR: total hip reconstruction. Ref./type
Proximal diaphysis
Neck
Medial
Lateral
Inferior
Case a Case b Case c [45]/in vivo Intact [15]/FEA antegrade nailing
−950μ −2550μ −1410μ
+410μ +1950μ +960μ +1200μ
−1590μ −1820μ −1640μ
[27]/in vitro retrograde nailing
−2800μ
[23]/in vitro Intact
−3800μ
+2200μ
−3700μ −900μ
−1000μ
+600μ
[18]/FEA Intact
−1500μ
+1150μ
[19]/FEA Intact
−700μ
+500μ
−1350μ
+1250μ +2500μ
[20]/FEA Intact [11]/FEA Intact
−1500μ
−1900μ
+2250μ
[28]/in vitro Intact
[9]/FEA THR
Material/loading/constraint
−750μ
−2750μ
+500μ
slotted nail having a lower bending stiffness failed due to plastic collapse. The unslotted nail, similar in geometry to our nail and loaded severely, did not undergo any significant geometry change but failed due to fatigue fracture. Considerably large differences in equivalent stress magnitude and distribution in the nail were found between the three cases, as shown in Fig. 4. The mid-diaphysis section of the nail is clearly under a state of plastic collapse, with von Mises stresses reaching 5730 MPa and 2180 MPa in cases a and b, respectively. Note that the nail material has a yield point of 870 MPa. In case c on the contrary, the most highly stressed locations are around the guide holes in the nail. Maximum equivalent stresses around the guide holes are shown in Table 3. At this level of stress, failure in case c is anticipated as fatigue around the most highly-stressed hole. In a study of mechanical failure in intramedullary interlocking nails [6], 17 nail failures out of 286 femoral nailings were reported. Most of these failures occurred due to mechanical fatigue around the nails’ distal guide holes. This was found to be in accordance with the stress levels of case c. In Table 3, the maximum equivalent stress around the nail guide holes were 552 MPa, 288 MPa, and 254 MPa for cases a, b and c, respectively. Note that all values were below the yield stress. Thus, cases a and b clearly do not reproduce the observed failure mode of the nail. They are simply unrealistic in comparison with case c. Stress contours were also observed along the interlocking pin surfaces, as shown in Fig. 5. In another FEA study about distal femoral fracture stabilization by retrograde IM nailing [16], a maximum equivalent stress of 629 MPa in the proximal and 191 MPa in the distal pins has been reported for the single-leg stance position. Their loading and boundary conditions matched nearly with those of case b. In Table 3, we read for case b a maximum equivalent stress of 210 MPa and 194 MPa for the proximal and distal pins, respectively. In Wu and Shih [3] it was found that the highest risk of failure occurred at the distal holes. All of our cases as well as [16] were short of predicting the location of highest stress and thus failure. They all predicted criticality on the proximal side rather than the distal.
Peak walking load. Linearly elastic isotropic, modulus ratio 10:0. Peak walking load applied via HJR + Abd. + VL Distally fixed. Synthetic. Peak walking load applied via HJR. Distally fixed. Synthetic. Peak walking load applied via HJR + Abd. + Iliotib. + VL Distally fixed. Synthetic. Single leg stance load applied via HJR + Abd + Iliops. + VL Distally fixed and head constrained. Linearly elastic isotropic, modulus ratio 17:1.5. Peak walking load applied via HJR + all thigh muscles. Distally fixed. Linearly elastic isotropic, modulus ratio 17:1.5. Partial walking load applied via HJR + all muscles. SD constraint set at the knee. Density-based elastic modulus. Peak walking load applied via HJR + all thigh muscles. Distally fixed. Linearly elastic isotropic, modulus ratio 18:1. Single leg stance applied via free-boundary condition approach. Linearly elastic isotropic, modulus ratio 17:1. Peak walking load applied via HJR + Abd. + Iliotib. + Iliops. Distally fixed.
The distribution of principal strains on the critical surface provided a means to evaluate the degree of loading of the bone and was of clinical relevance. Principal strain components at various aspects of the bone by a number of references are tabulated in Table 5 for comparison. The locations where strains were most frequently reported included the medial and lateral aspects of the proximal diaphysis and the interior (medial) aspect of the neck. A majority of the studies were FEA. Additionally, there were three studies involving in vitro experiments, and one in vivo study. In all but one of the FEA studies, a linearly elastic and isotropic material model was used. An in vivo peak principal strain of +1200μ at the proximal lateral femoral aspect of a walking patient (weighing approximately 65 kg) was reported in Aamodt et al. [45]. Of our three cases, case c was in best agreement with a peak principal strain of +960μ. Interestingly, our strain reading was 20% lower than the in vivo one despite the use of a heavier patient (weighing 87 kg) in our model. This meant that either the cortical elastic modulus or the cortical shell thickness was under-estimated by our model, resulting in a more compliant response than what would be expected. Two other FEA simulations in Table 5 [18,19] were also in good agreement with the in vivo strain. (Note that the reduced strain of [19] was a result of partial loading of that model.) In both, all the rigid-body degrees-of-freedom of the femur were eliminated, although a head constraint was not utilized. In addition, a consistent self-equilibrating loading scheme including all thigh muscles was used. In contrast, we have used only the hip-joint reaction and dominant muscular action in the proximal aspect in case c which was still in good agreement with [45]. The strains in cases a and b were unrealistically high. Thus, distally fixing the entire femur and/or not including the active muscles produced erroneous strains. Although the knee joint essentially has six degrees of freedom, its movement is restrained in many directions due to its complex ligamentous structure. For example, anterior and posterior cruciate ligaments constrain A-P translation of the knee [46]. Of the soft tissues
Please cite this article as: R. Bayoglu, A.F. Okyar, Implementation of boundary conditions in modeling the femur is critical for the evaluation of distal intramedullary nailing, Medical Engineering and Physics (2015), http://dx.doi.org/10.1016/j.medengphy.2015.08.007
JID: JJBE
ARTICLE IN PRESS
[m5G;August 30, 2015;13:54]
R. Bayoglu, A.F. Okyar / Medical Engineering and Physics 000 (2015) 1–8
that attach to the lateral side of the femur, the popliteus muscle– tendon unit originates from lateral femoral epicondyle and restrains anterior translation [46] and popliteofibular and lateral collateral ligaments restrain posterior translation [47,48]. Point N at the distal lateral epicondyle corresponded approximately to a location between the popliteus muscles’ and lateral collateral ligaments’ attachment sites. In case c, this point was constrained in the A-P direction to represent the function of these ligaments. Instead of over-constraining the femur by fixing the distal part entirely, as in cases a and b, using the set of boundary conditions in case c provided empirically realistic results. Including all muscles in an experimental set-up or a finite element environment is a complex process, making the controllability and reproducibility of these tests difficult. Results showed that case c produced plausible levels of deflection, nail stress and cortical strain. Moreover, the relative motion at the fracture site was significantly lower in comparison with the other cases. The mode of nail failure was also correctly predicted. From an engineering point of view, we conclude that the application of dominant muscular actions in addition to restraining the head, the knee and the distal lateral epicondyle, as shown in Speirs et al. [17], was an effective way to carry out a physiologically more realistic FEA compared with models that did not do so. Conflict of interest None declared. Funding The research was conducted in the Biomechanics Research Laboratory located in the Faculty of Engineering at the Yeditepe University. The software and hardware used for the purposes of conducting this research was paid for by the Research and Development Office of the Yeditepe University. Ethical approval Not required. References [1] Boenisch UW, de Boer PG, Journeaux SF. Unreamed intramedullary tibial nailing– fatigue of locking bolts. Injury 1996;27(4):265–70. [2] Kneifel T, Buckley R. A comparison of one versus two distal locking screws in tibial fractures treated with unreamed tibial nails: a prospective randomized clinical trial. Injury 1996;27(4):271–3. [3] Wu C-C, Shih C-H. Biomechanical analysis of the mechanism of interlocking nail failure. Arch Orthop Traum Su 1992;111(5):268–72. doi:10.1007/BF00571522. [4] Griza S, Zimmer CG, Reguly A, Strohaecker TR. A case study of subsequential intramedullary nails failure. Eng Failure Anal 2009;16(3):728–32. [5] Zimmerman KW, Klasen HJ. Mechanical failure of intramedullary nails after fracture union. J Bone Joint Surg Br 1983;65-B(3):274–5. [6] Bhat AK, Rao SK, Bhaskaranand K. Mechanical failure in intramedullary interlocking nails. J Orthop Surg (Hong Kong) 2006;14(2):138–41. [7] Augat P, Burger J, Schorlemmer S, Henke T, Peraus M, Claes L. Shear movement at the fracture site delays healing in a diaphyseal fracture model. J Orthop Res 2003;21(6):1011–17. doi:10.1016/S0736-0266(03)00098-6. [8] Duda GN, Kirchner H, Wilke H-J, Claes L. A method to determine the 3-d stiffness of fracture fixation devices and its application to predict inter-fragmentary movement. J Biomech 1997;31(3):247–52. [9] Stolk J, Verdonschot N, Huiskes R. Hip-joint and abductor-muscle forces adequately represent in vivo loading of a cemented total hip reconstruction. J Biomech 2001;34(7):917–26. http://dx.doi.org/10.1016/S0021-9290(00)002256. http://www.sciencedirect.com/science/article/pii/S0021929000002256. [10] Tupis TM, Altman GT, Altman DT, Cook HA, Miller MC. Femoral bone strains during antegrade nailing: a comparison of two entry points with identical nails using finite element analysis. Clin Biomech 2012;27(4):354–9. http://dx.doi.org/ 10.1016/j.clinbiomech.2011.11.002. http://www.sciencedirect.com/science/article/ pii/S0268003311002907. [11] Taylor ME, Tanner KE, Freeman MAR, Yettram AL. Stress and strain distribution within the intact femur: compression or bending? Med Eng Phys 1996;18(2):122– 31.
7
[12] Papathanasopoulou V, Fotiadis D, Massalas C. Intact and implanted femur behaviour during walking and jogging. In: Engineering in medicine and biology society, 2001. Proceedings of the 23rd annual international conference of the IEEE, 2. IEEE; 2001. p. 1524–7. [13] Cheung G, Zalzal P, Bhandari M, Spelt JK, Papini M. Finite element analysis of a femoral retrograde intramedullary nail subject to gait loading. Med Eng Phys 2004;26(2):93–108. [14] Kajzer W, Kajzer A, Marciniak J. Fem analysis of expandable intramedullary nails in healthy and osteoporotic femur. J Achievements Mater Manufac Eng 2009;37(2):563–70. [15] Montanini R, Filardi V. In vitro biomechanical evaluation of antegrade femoral nailing at early and late postoperative stages. Med Eng Phys 2010;32(8):889–97. [16] Shih K-S, Hsu C-C, Hsu T-P, Hou S-M, Liaw C-K. Biomechanical analyses of static and dynamic fixation techniques of retrograde interlocking femoral nailing using nonlinear finite element methods. Comput Meth Prog Biomed 2014; 113(2):456–64. doi:10.1016/j.cmpb.2013.11.002. [17] Speirs AD, Heller MO, Duda GN, Taylor WR. Physiologically based boundary conditions in finite element modelling. J Biomech 2007;40(10):2318–23. [18] Duda GN, Heller M, Albinger J, Schulz O, Schneider E, Claes L. Influence of muscle forces on femoral strain distribution. J Biomech 1998;31(9):841–6. [19] Polgar K, Gill HS, Viceconti M, Murray DW, O’Connor JJ. Strain distribution within the human femur due to physiological and simplified loading: finite element analysis using the muscle standardized femur model. Proc Inst Mech Eng H 2003;217(3):173–89. [20] Phillips ATM. The femur as a musculo-skeletal construct: A free boundary condition modelling approach. Med Eng Phys 2009;31(6):673–80. [21] George CJ, Lindsey RW, Noble PC, Alexander JW, Kamaric E. Optimal location of a single distal interlocking screw in intramedullary nailing of distal third femoral shaft fractures. J Orthop Traum 1998;12(4):267–72. [22] Schandelmaier P, Farouk O, Krettek C, Reimers N, Mannss J, Tscherne H. Biomechanics of femoral interlocking nails. Injury 2000;31(6):437–43. [23] Szivek JA, Benjamin JB, Anderson PL. An experimental method for the application of lateral muscle loading and its effect on femoral strain distributions. Med Eng Phys 2000;22(2):109–16. [24] Schneider E, Michel MC, Genge M, Zuber K, Ganz R, Perren SM. Loads acting in an intramedullary nail during fracture healing in the human femur. J Biomech 2001;34(7):849–57. [25] Wang G, Pan T, Peng X, Wang J. A new intramedullary nailing device for the treatment of femoral shaft fractures: a biomechanical study. Clin Biomech 2008;23(3):305–12. [26] Kajzer W, Kajzer A, Marciniak J. Expandable intramedullary nail – experimental biomechanical evaluation. Arch Mater Sci Eng 2010;41(1):45–52. [27] Hak DJ, Neiman R, Hazelwood S. Biomechanical strain analysis of the proximal femur following retrograde intramedullary nailing. Curr Orthop Pract 2010;21(4):385–9. http://dx.doi.org/10.1097/BCO.0b013e3181d73bae. [28] Simoes JA, Vaz MA, Blatcher S, Taylor M. Influence of head constraint and muscle forces on the strain distribution within the intact femur. Med Eng Phys 2000;22(7):453–9. [29] Court-Brown CM, Caeser B. Epidemiology of adult fractures: A review. Injury 2006;37:691–7. doi:10.1016/j.injury.2006.04.130. [30] Ehlinger M, Ducrot G, Adam P, Bonnomet F. Distal femur fractures. surgical techniques and a review of the literature. Orthop Traum Surg Res 2013;99(3):353– 60. http://dx.doi.org/10.1016/j.otsr.2012.10.014. http://www.sciencedirect.com/ science/article/pii/S1877056813000200. [31] ADINA R&D, Inc. Release 8.9, Watertown, MA, USA; 2013. [32] Bergmann G, Deuretzbacher G, Heller M, Graichen F, Rohlmann A, Strauss J, et al. Hip contact forces and gait patterns from routine activities. J Biomech 2001;34:859–71. [33] Chen SH, Yu TC, Chang CH, Lu YC. Biomechanical analysis of retrograde intramedullary nail fixation in distal femoral fractures. The Knee 2008;15(5):384–9. [34] Heller MO, Bergmann G, Kassi JP, Claes L, Haas NP, Duda GN. Determination of muscle loading at the hip joint for use in pre-clinical testing. J Biomech 2005;38(5):1155–63. [35] Horsman MDK, Koopman HFJM, van der Helm FCT, Pros LP, Veeger HEJ. Morphological muscle and joint parameters for musculoskeletal modelling of the lower extremity. Clin Biomech 2007;22(2):239–47. http://dx.doi.org/10.1016/ j.clinbiomech.2006.10.003. http://www.sciencedirect.com/science/article/pii/ S0268003306001896. [36] Morlock M, Schneider E, Bluhm A, Vollmer M, Bergmann G, Muller V, et al. Duration and frequency of every day activities in total hip patients. J Biomech 2001;34(7):873–81. [37] Bergmann G., editor, 2002. HIP98 – Loading of the hip joint. Free University, Berlin, ISBN 3-9807848-0-0; 1998. [38] Bayoglu R, Okyar AF. A physiologically accurate mechanical representation of the bone-implant construct under gait loads. In: Proceedings of the sixth national biomechanics congress, Sakarya University, SAUFBE, vol. 16 (3); 2012. p. 136–43. [39] Grant C. Mechanical testing and modelling of a bone-implant construct: contemporary methods and analysis. Queensland University of Technology; 2012. PhD Thesis. Brisbane, Australia. [40] Eberle S, Gerber C, von Eldenburg G, Hungerer S, Augat P. Type of hip fracture determines load share in intramedullary osteosynthesis. Clin Orthop Relat Res 2009;497(8):1972–80. [41] Material Property Data; (2014). URL http://www.matweb.com. [42] McKibbin B. The biology of fracture healing in long bones. J Bone Joint Surg Br 1978;60-B(2):150–62. http://www.bjj.boneandjoint.org.uk/content/60B/2/150.full.pdf. http://www.bjj.boneandjoint.org.uk/content/60-B/2/150.short.
Please cite this article as: R. Bayoglu, A.F. Okyar, Implementation of boundary conditions in modeling the femur is critical for the evaluation of distal intramedullary nailing, Medical Engineering and Physics (2015), http://dx.doi.org/10.1016/j.medengphy.2015.08.007
JID: JJBE 8
ARTICLE IN PRESS
[m5G;August 30, 2015;13:54]
R. Bayoglu, A.F. Okyar / Medical Engineering and Physics 000 (2015) 1–8
[43] Rodriguez EK, Boulton C, Weaver MJ, Herder LM, Chacko JHMAT, Appleton PT, et al. Predictive factors of distal femoral fracture nonunion after lateral locked plating: a retrospective multicenter case-control study of 283 fractures. Injury 2014;45(3):554–9. doi:10.1016/j.injury.2013.10.042. [44] Kyle R. Biomechanics of intramedullary fracture fixation. Orthopedics 1985;8(11):13561359. http://europepmc.org/abstract/MED/3832024. [45] Aamodt A, Lund-Larsen J, Eine J, Andersen E, Benum P, Husby OS. In vivo measurements show tensile axial strain in the proximal lateral aspect of the human femur. J Orthop Res 1997;15:927–31. [46] Halewood C, Amis A. Clinically relevant biomechanics of the knee capsule and ligaments. Knee Surg Sports Traumatol Arthrosc 2015. doi:10.1007/s00167-0153594-8.
[47] Veltri DM, Deng X-H, Torzilli PA, Warren RF, Maynard MJ. The role of the cruciate and posterolateral ligaments in stability of the knee: a biomechanical study. Am J Sport Med 1995;23(4):436–43. http://ajs.sagepub.com/content/23/4/436. full.pdf. doi:10.1177/036354659502300411. http://ajs.sagepub.com/content/23/ 4/436.abstract. [48] Shahane SA, Ibbotson C, Strachan R, Bickerstaff D. The popliteofibular ligament: An anatomical study of the posterolateral corner of the knee. J Bone Joint Surg Br 1999;81-B(4):636–42. http://www.bjj.boneandjoint.org.uk/content/81-B/4/636. full.pdf. http://www.bjj.boneandjoint.org.uk/content/81-B/4/636.abstract.
Please cite this article as: R. Bayoglu, A.F. Okyar, Implementation of boundary conditions in modeling the femur is critical for the evaluation of distal intramedullary nailing, Medical Engineering and Physics (2015), http://dx.doi.org/10.1016/j.medengphy.2015.08.007